DressingWhisk vinegar, mustard, and sugar in a small bowl until sugar is dissolved. Whisking constantly, gradually add olive oil and then walnut oil; whisk until emulsified. Add bacon; season with salt and pepper.Do Ahead: Dressing can be made 1 day ahead. Cover and chill.

Toss frisée, kale, chicken, bacon, raisins, and nuts with dressing in a very large bowl. Season with salt and pepper. Add eggs, apple, cheddar, and spinach; taste and season again with salt and pepper. Divide among plates.